Teaching Stats for Data Science

Bridges and roommates

Should we be roomies?

• We’ll have to give up some space.
• We’ll need to adopt some good data habits.
• We’ll have to learn to talk with guests our roommate invites over:
  • large observational datasets
  • frequent interest in causation
  • guiding decision-making rather than rejecting hypothesis.
• Since our rooms are small, a lot of our stuff will be in the living room and kitchen for everyone to use.

Proposal for the move:







Pack up our stuff into ten boxes

Ten stat boxes

                  K = for kitchen, LR = for living room

Instead, this

• Rich graphics, incl. color, tranparency, faceting, …
• Relationships among multiple variables

NHANES %>% 
  gf_point(Height ~ Age | Gender, color = ~ Gender, alpha = 0.1)

• Inputs and output, explanatory and response variables

height(Age = 25, Gender = "female")

##   Gender Age model_output
## 1 female  25     164.8456

height(Age = 3:80, Gender = c("female", "male")) %>% 
  gf_line(model_output ~ Age | Gender)

Model Training: tools for building functions that look like your data

hmod1 <- lm(Height ~ Gender * ns(Age, 5), data = NHANES) 

• Make it about different architectures, e.g. CART, Random Forest, Logistic regression, …
• Both regression models and classifiers
• Encourage nonlinearity (ns() == “not straight”?)

wmod1 <- glm(outcome == "Dead" ~ smoker, data = Whickham,                    family = "binomial")
mod_effect(wmod1, ~ smoker, age = c(40, 50, 60))

##        change smoker to:smoker
## 1 -0.07537604     No       Yes

wmod2 <- glm(outcome == "Dead" ~ smoker + age, data = Whickham,                 family = "binomial")
mod_effect(wmod2, ~ smoker, age = c(40, 50, 60))

##       change smoker to:smoker age
## 1 0.01377155     No       Yes  40
## 2 0.03419996     No       Yes  50
## 3 0.05105680     No       Yes  60

NHANES %>% df_stats(Height ~ Gender, coverage(0.95))

##   Gender  lower upper
## 1 female 102.43 176.1
## 2   male 100.90 190.3

NHANES %>%
  gf_jitter(Height ~ Gender, alpha = 0.05, width = 0.15) %>%
  gf_violin(alpha = 0.3, fill = ~ Gender, color = NA)

hmod_ensemble <- mod_ensemble(hmod1, nreps = 4)
mod_effect(hmod_ensemble, ~ Age, Age = 5, step = 1, 
           Gender = c("male", "female")) %>%
  arrange(Gender)

##      slope Age to:Age Gender bootstrap_rep
## 1 6.442775   5      6 female             1
## 2 6.394813   5      6 female             2
## 3 6.415638   5      6 female             3
## 4 6.396559   5      6 female             4
## 5 7.254420   5      6   male             1
## 6 7.258021   5      6   male             2
## 7 7.248615   5      6   male             3
## 8 7.233795   5      6   male             4

mod_eval(hmod1, data = NHANES) %>%
  df_stats( ~ I((model_output - Height)^2), mean)

## [1] 52.14731

Or make it a fundamental operation.

mod_error(hmod1, testdata = NHANES)

## [1] 52.14731

Let’s try another model that’s more flexile

hmod2 <- lm(Height ~ Gender * ns(Age, 25), data = NHANES) 

How does it compare to the original?

mod_cv(hmod1, hmod2, ntrials = 50) %>% 
  df_stats(mse ~ model, coverage(0.95))

##   model    lower    upper
## 1 hmod1 52.21514 52.30473
## 2 hmod2 49.72174 49.86336

• It’s still important to talk about how to collect meaningful data to form conclusions that generalize outside the sample at hand.
• Many data-science applications involve reasoning about causal influences.
  • We need to come down from the mathematical high horse of “no causation without experimentation.”
  • Recognize responsible methods for addressing causation.

e.g. the Judea Pearl award in causality education

… and of course